Question: Simplify the following expression: $ y = \dfrac{-3}{5} + \dfrac{4a + 9}{-3a + 6} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3a + 6}{-3a + 6}$ $ \dfrac{-3}{5} \times \dfrac{-3a + 6}{-3a + 6} = \dfrac{9a - 18}{-15a + 30} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{4a + 9}{-3a + 6} \times \dfrac{5}{5} = \dfrac{20a + 45}{-15a + 30} $ Therefore $ y = \dfrac{9a - 18}{-15a + 30} + \dfrac{20a + 45}{-15a + 30} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{9a - 18 + 20a + 45}{-15a + 30} $ $y = \dfrac{29a + 27}{-15a + 30}$ Simplify the expression by dividing the numerator and denominator by -1: $y = \dfrac{-29a - 27}{15a - 30}$